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Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads

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Abstract

We study minmax due-date based on common flow-allowance assignment and scheduling problems on a single machine, and extend known results in scheduling theory by considering convex resource allocation. The total cost function of a given job consists of its earliness, tardiness and flow-allowance cost components. Thus, the common flow-allowance and the actual jobs’ processing times are decision variables, implying that the due-dates and actual processing times can be controlled by allocating additional resource to the job operations. Consequently, our goal is to optimize a cost function by seeking the optimal job sequence, the optimal job-dependent due-dates along with the actual processing times. In all addressed problems we aim to minimize the maximal cost among all the jobs subject to a constraint on the resource consumption. We start by analyzing and solving the problem with position-independent workloads and then proceed to position-dependent workloads. Finally, the results are generalized to the method of common due-window. For all studied problems closed form solutions are provided, leading to polynomial time solutions.

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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  1. Department of Economics and Business Administration, Ariel University, 40700, Ariel, Israel

    Baruch Mor

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  1. Baruch Mor
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Correspondence to Baruch Mor.

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Mor, B. Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads. J Comb Optim 43, 79–97 (2022). https://doi.org/10.1007/s10878-021-00746-w

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